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2017 is not just another prime number

295 points| tjwei | 9 years ago |weijr-note.blogspot.com | reply

59 comments

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[+] williamstein|9 years ago|reply
Verifications of all the statements using SageMath, in case you want to be convinced or explore further: https://cloud.sagemath.com/projects/4a5f0542-5873-4eed-a85c-...
[+] ComodoHacker|9 years ago|reply
> 2017 can be written as a sum of cubes of five distinct integers.

This gives no results in SageMath...

[+] joeax|9 years ago|reply
Meh. A prime number year last happened in 2011. Just kidding... happy new prime number year!

BTW I'm really looking forward to the next perfect square year: 2025 (45^2). It last happened in 1936, and won't happen again until 2116.

[+] ClashTheBunny|9 years ago|reply
I'm hoping to to see the only power of two in a millennium: 2048
[+] aisofteng|9 years ago|reply
It would be an interesting exercise to consider the years that are a perfect square n^2 and then try to give some sort of attempt at dividing history into n segments of n years, trying to find a common theme for each segment.
[+] kondbg|9 years ago|reply
> The sum of the cube of gap of primes up to 2017 is a prime number. That is (3-2)^3 + (5-3)^3 + (7-5)^3 + (11-7)^3 + ... + (2017-2011)^3 is a prime number.

For the non-mathematically inclined, how do mathematicians come up with these? Are these just observations that they happened to witness, or are there underlying theoretical properties that allow one to derive this claim?

[+] indexerror|9 years ago|reply
There has been a great amount of research to find ways to check if a number of prime or not in polynomial time[1]. Many of such _facts_ are a observations from this conquest. Number theory reveals fascinating facts about spacing in prime numbers determining properties within a range. Sometimes such results emerge from there.

1: https://en.wikipedia.org/wiki/Primality_test

[+] ChuckMcM|9 years ago|reply
They forgot to calculate how many certificates on the Internet use 2017 as one of their primes :-)
[+] vog|9 years ago|reply
Or, how many use a prime <= 2017, for that matter.
[+] kahrkunne|9 years ago|reply
What I always wonder though, is 2017 really a special number or can you fit things like this to every number?
[+] Houshalter|9 years ago|reply
What I like to do to measure the "mathematical interestingness" of a number, is check how many times it appears in OEIS. A database of sequences of numbers found in mathematical research. 2017 appeared in 453 sequences. For comparison; 2016 appears 833 sequences, and 2018 appears in 113.

http://oeis.org/search?q=seq%3A2016&sort=&language=english&g...

[+] tjwei|9 years ago|reply
Reminds me of "Interesting number paradox" :p This can be considered as a proof that every number is interesting.

IMHO, being a prime number might give 2017 some advantages, and 2017 might be a slightly more interesting than most of prime numbers.

[+] rosstex|9 years ago|reply
I’m feeling more excited about this year already!
[+] tpogge|9 years ago|reply
2017 is the sum of five distinct cubes TWICE OVER: 2017 = 10^3 + 9^3 + 6^3 + 4^3 + 2^3. 2017 = 12^3 + 6^3 + 4^3 + 2^3 + 1^3. As a bonus, it's also the sum of EIGHT DISTINCT CUBES: 2017 = 9^3 + 8^3 + 7^3 + 6^3 + 5^3 + 4^3 + 3^3 + 1^3.
[+] duomono4|9 years ago|reply
* (loop for i from 1 to 15 do (loop for i2 from i to 15 do (loop for i3 from i2 to 15 do (loop for i4 from i3 to 15 do (loop for i5 from i4 to 15 do (if (= (+ (* i i i) (* i2 i2 i2) (* i3 i3 i3) (* i4 i4 i4) (* i5 i5 i5)) 2017) (print (list i i2 i3 i4 i5))))))))

(1 2 2 10 10) (1 2 4 6 12) (2 4 6 9 10) NIL

[+] peter303|9 years ago|reply
Definately a case of OCD. I am guilty of it too while interpreting license plate numbers in boring traffic.
[+] warent|9 years ago|reply
Nice! Although I think it's amusing that they said "odd primes" as if there's any even primes
[+] otalp|9 years ago|reply
2 is a prime number...